Transformations on the
coordinate plane
Transformations Review
Type
A translation moves a
figure left, right, up, or
down
A reflection moves a
figure across its line of
reflection to create its
mirror image.
A rotation moves a
figure around a given
point.
Diagram
Now we will look at how each
transformation looks on a coordinate
plane. The transformed figure is often
named with the same letters, but adding
an apostrophe. The transformation of
ABC is A’B’C’.
Translation
Translate ABC 6 units to the right.
Find point A and
count 6 units to the
right. Plot point A’.
Find point B and
count 6 units to the
right. Plot point B’.
Find point C and
count 6 units to the
right. Plot point C’.
6 Units
A
A’
B’
B
C
C’
Translation Rules
•To translate a figure a units to the right,
increase the x-coordinate of each point by a
amount.
•To
translate
a figure
to the
left,right.
Translate
point
P (3,a2)units
9 units
to the
decrease
each
Since we the
arex-coordinate
going to the of
right,
wepoint
add by
9 toa
amount.
the x-coordinate. 3 + 9 = 12, so the new
Translate
point P (3,
units
coordinates
of 2)
P’ 6are
(12,to2)the left.
Since we are going up, we subtract 6 to the xcoordinate. 3 - 6 = -3, so the new coordinates
of P’ are (-3, 2)
Translation Rules
•To translate a figure a units up, increase the
y-coordinate of each point by a amount.
•To translate
a figure
a (3,
units
Translate
point P
2) down,
9 unitsdecrease
up.
the
y-coordinate
of each
by 9a to
amount.
Since
we are going
up, point
we add
the yTranslate
point
P 9(3,= 2)
units
coordinate.
2+
11,6so
thedown.
new
Since we coordinates
are going down,
of P’ we
aresubtract
(3, 11) 6 to the
y-coordinate. 2 - 6 = -4, so the new
coordinates of P’ are (3, -4)
Translation Example 2
The coordinates of Since we are
-5 + 6 = 1, so the
point A are (-5, 4) moving to the right new coordinates
we increase the x- of A’ are (1, 4).
coordinate by 6.
The coordinates of Since we are
-2 + 6 = 4, so the
point B are (-2, 3) moving to the right new coordinates
we increase the x- of B’ are (4, 3).
coordinate by 6.
The coordinates of Since we are
-3 + 6 = 3, so the
point C are (-3, 1) moving to the right new coordinates
we increase the x- of C’ are (3, 1).
coordinate by 6.
Practice
• Point P (5, 8). Translate 2 to the left and 6
up. P’ (3, 14)
• Point Z (-3, -6). Translate 5 to the right
and 9 down.
Z’ (2, -15)
• Translate LMN, whose coordinates are
(3, 6), (5, 9), and (7, 12), 9 units left and
14 units up.
L’M’N’ (-6, 20), (-4, 23), (-2, 26)
Reflection
Reflect ABC across the y-axis.
Count the number of units point A
is from the line of reflection.
Count the same number of units on
the other side and plot point A’.
Count the number of units point B
is from the line of reflection.
Count the same number of units on
the other side and plot point B’.
Count the number of units point C
is from the line of reflection.
Count the same number of units on
the other side and plot point C’.
A
5 Units
5 Units
2 Units 2 Units
B
3 Units
C
B’
3 Units
C’
A’
Reflection Rules
•To reflect point (a, b) across the y-axis use
the opposite of the x-coordinate and keep
the y coordinate the same.
P (3,
across
y-axis.
•ToReflect
reflect point (a,
b) 2)
across
thethe
x-axis
keep
Since
we reflecting
the use
y-axis.
the
x-coordinate
the across
same and
the Keep
the
y the same
use the opposite of the x.
opposite
of the and
y-coordinate
(-3,
Reflect point P (3,
2)2)
across the x-axis.
Since we reflecting across the x-axis. Keep
the x the same and use the opposite of the y.
(3, -2)
Practice
The coordinates of ABC are:
(-5, 4), (-2, 3), (-3, 1)
Reflect ABC across the y-axis and
then reflect it across the x-axis.
To reflect it across the y-axis keep the y the same
and use the opposite x. The new coordinates are:
(5, 4), (2, 3), (3, 1)
To reflect it across the x-axis keep the x the same
and use the opposite y. The new coordinates are:
(5, -4), (2, -3), (3, -1)
Rotation Rules
•To rotate a point 90° clockwise, switch the
coordinates, and then multiply the new ycoordinate by -1.
•To rotate
a point
just multiply
Rotate
point
P (3, 180°,
2) clockwise
abouteach
the origin.
coordinate
by rotating
-1.
Since we are
it clockwise, we switch
Rotate
point P (3,(2,
2)3)
clockwise
about
origin.
the coordinates
and multiply
thethe
new
y
Since
wethe
arenew
rotating
it 180°, we
by
-1, so
coordinates
aresimply
(2, -3)
multiply the coordinates by -1, so the new
coordinates are (-3, -2).
Practice
• Point P (5, 8). Rotate 90° clockwise about
the origin.
P’ (8, -5)
• Point Z (-3, -6). Rotate 180° about the
origin.
Z’ (-3, -6)
• Rotate LMN, whose coordinates are (3,
6), (5, 9), and (7, 12), 90° clockwise about
the origin.
L’M’N’ (6, -3), (9, -5), (7, -12)